Paint over Render in compositor
By creating a new image in the UV/Image editor and using a mixRGB node to mix it with the render layer you can get the same result as a photoshop layer. Each image created and mixed in using the compositor will correspond to one layer in PS. You will find each blend type of the mix node will correspond to a layer mode in PS. The alpha of the image or a separate image can be connected to the fac of the mix node for a layer mask. We can also create and animate a mask. While the render result or viewer node preview doesn't update as you paint, it does update after you complete each stroke.

So while we don't get the simplicity of the way layers are presented and edited in the same location, we can get the same end results, even with some extra flexibility in how they are combined by using blenders compositor node system. The other factor to differentiate PS and blender will be the amount of painting tools available.